2-D Niblett-Bostick magnetotelluric inversion - MTNet

J. RODRÍGUEZ et al. 2-D Niblett-Bostick
80% if the algorithm could not accommodate the static
shift into the structure. As can be observed in Fig. 9B, the
model for the perturbed data presents basically the same
broad features of the two main conductive anomalies. The
static shift is accommodated mainly by means of extra
variations of conductivity at shallow depths, as expected.
This is highlighted in Fig. 10 that shows a zoom view of
the first 5 km of the model. The static shift surfaces as high
frequency lateral features, over the already highly variable
top conductive surface layer. Similar results, with somewhat
broader features, are obtained with a larger window. This
is illustrated in Fig. 11 for the complete model, with and
without extra static contamination.
CONCLUSIONS
The present application builds on the well-known
Niblett-Bostick approximation for 1-D soundings. Our
intention has been to show that such an approximation is
viable in higher dimensions, both on theoretical and practical
grounds. Most quantities involved are analytical as far as
they can be; the use of series and parallel impedances avoid
elaborated processing of the data prior to interpretation
and the RHANN square window approach allows for the
computation of averages in a simple fashion. We feel that
these features can make the present approximation a fair
extension of the popular Niblett-Bostick transformation.
Parallel impedances, in particular, are recommended as
standard practice for the approximation.
ACKNOWLEDGMENTS
We would like to thank Colin Farquharson and Josef Pek for
their comments and suggestions for improving the manuscript.
Joel Rodríguez-Ramírez thanks the Consejo Nacional de Ciencia y
Tecnología México (CONACYT) for funding his doctoral studies
(scholarship #94748). We also thank CONACYT for Grant #47922.
REFERENCES
Anderson, W.L., 1975. Improved digital filters for evaluating
Fourier and Hankel transform integrals. United States
Geological Survey Report USGS-GD-75-012., 223 pp.
Backus, G.E., Gilbert, J.F., 1968. The resolving power of gross
earth data. Geophysical Journal of the Royal Astronomical
Society, 16, 169-205.
Backus, G.E., Gilbert, J.F., 1970. Uniqueness in the inversion of
inaccurate gross earth data. Philosophical Transactions of the
Royal Society of London, A266, 123-192.
Bailey, R.C., 1970. Inversion of the geomagnetic induction
problem. Proceedings of the Royal Society of London, A315,
185-194.
Geologica Acta, 8(1), 15-30 (2010)
DOI: 10.1344/105.000001513
Boerner, D.E., Holladay, J.S., 1990. Approximate Fréchet
derivatives in inductive electromagnetic soundings.
Geophysics, 55, 1589-1595.
Bostick, F.X., 1977. A simple almost exact method of
magnetotelluric analysis. In: Ward, S. (ed.). Workshop on
Electrical Methods in Geothermal Exploration. United States
Geological Survey, Contract Nº. 14080001-G-359, 174-183.
Brunner, I., Friedel, S., Jacobs F., Danckwardt, E., 2003.
Investigation of a tertiary maar structure using threedimensional
resistivity imaging. Geophysical Journal
International, 136, 771-780.
Cagniard, L., 1953. Basic theory of the magneto-telluric method
of geophysical prospecting. Geophysics, 18, 605-635.
Christensen, N.B., 1997. Electromagnetic subsurface imaging
- A case for an adaptive Born approximation. Surveys in
Geophysics, 18, 441-510.
De Groot-Hedlin, C.D., Constable, S.C., 1990. Occam’s
inversion to generate smooth, two-dimensional models from
magnetotelluric data. Geophysics, 55, 1613-1624.
Esparza, F.J., 1991. Sufficiency of Maxwell’s equations in relation
with electromagnetic inverse problems. Doctoral thesis.
México, Centro de Investigación Científica y de Educación
Superior de Ensenada, 90 pp.
Esparza, F.J., Gómez-Treviño, E., 1996. Inversion of
magnetotelluric soundings using a new integral form of the
induction equation. Geophysical Journal International, 127,
452-460.
Friedel, S., 2003. Resolution, stability and efficiency of resistivity
tomography estimated from a generalized inverse approach.
Geophysical Journal International, 153, 305-316.
Gómez-Treviño, E., 1987a. Nonlinear integral equations for
electromagnetic inverse problems. Geophysics, 52, 1297-
1302.
Gómez-Treviño, E., 1987b. A simple sensitivity analysis of
time-domain and frequency-domain electromagnetic
measurements. Geophysics, 52, 1418-1423.
Gómez-Treviño, E., 1996. Approximate depth averages of
electrical conductivity from surface magnetotelluric data.
Geophysical Journal International, 127, 762-772.
Hidalgo, H., Gómez-Treviño, E., 1996. Application of constructive
learning algorithms to the inverse problem. Institute of
Electrical and Electronics Engineers (IEEE), Transactions on
Geoscience and Remote Sensing, 34, 874-885.
Hohmann, G.W., 1971. Electromagnetic Scattering by conductors
in the earth near a line source of current. Geophysics, 36, 101-
131.
Hopfield, J.J., 1982. Neural Networks and physical systems with
emergent collective computational abilities. United States of
America, Proceedings of the National Academy of Sciences,
79, 2554-2558.
Ising, E., 1925. Beitrag zur theorie des ferromagnetismus.
Zeitschrift für Physik, 31, 253-258.
Jones, A.G., 1983. On the the equivalence on the Niblett and
Bostick transformation in the magnetotelluric method.
Journal of Geophysics, 53, 72-73.
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